Three-dimensional topological phase on the diamond lattice

Abstract

An interacting bosonic model of Kitaev type is proposed on the three-dimensional diamond lattice. Similarly to the two-dimensional Kitaev model on the honeycomb lattice which exhibits both Abelian and non-Abelian phases, the model has two (``weak'' and ``strong'' pairing) phases. In the weak pairing phase, the auxiliary Majorana hopping problem is in a topological superconducting phase characterized by a non-zero winding number introduced in A. P. Schnyder, S. Ryu, A. Furusaki, and A. W. W. Ludwig, arXiv:0803.2786. The topological character of the weak pairing phase is protected by a discrete symmetry.

7 pages, 5 figures

References in corpus (32)

• Quantum Spin Hall Effect in Graphene
• Fault-tolerant quantum computation by anyons
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Anyons in an exactly solved model and beyond
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological invariants of time-reversal-invariant band structures
• Quantum Spin Hall Effect
• Controlling Spin Exchange Interactions of Ultracold Atoms in Optical Lattices
• A toolbox for lattice spin models with polar molecules
• Topological Mott Insulators
• Riemannian symmetric superspaces and their origin in random matrix theory
• Exact results for spin dynamics and fractionization in the Kitaev Model
• The Flux-Phase of the Half-Filled Band
• An exact chiral spin liquid with non-Abelian anyons
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Fermions, strings, and gauge fields in lattice spin models
• Exactly solvable Kitaev model in three dimensions
• Edge solitons of topological insulators and fractionalized quasiparticles in two dimensions
• Symmetry classes of disordered fermions
• Majorana Fermions, Exact Mappings between Classical and Topological Orders
• String and Membrane condensation on 3D lattices
• Emergent Fermions and Anyons in the Kitaev Model
• Creation and Manipulation of Anyons in the Kitaev Model
• Anyonic Loops in Three Dimensional Spin liquid and Chiral Spin Liquid
• An exactly soluble model with tunable p-wave paired fermion ground states

Cited by in corpus (47)

• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantum Spin Liquid States
• Entanglement entropy and entanglement spectrum of the Kitaev model
• Three-dimensional topological lattice models with surface anyons
• Classification of gapless Z2 spin liquids in three-dimensional Kitaev models
• Disorder in a quantum spin liquid: flux binding and local moment formation
• Quantum spin liquid with a Majorana Fermi surface on the three-dimensional hyperoctagon lattice
• Topologically stable gapless phases of time-reversal invariant superconductors
• Microscopic models for Kitaev's sixteenfold way of anyon theories
• A $\Gamma$-matrix generalization of the Kitaev model
• Bosonization in three spatial dimensions and a 2-form gauge theory
• Exact Chiral Spin Liquid with Stable Spin Fermi Surface on the Kagome Lattice
• Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
• Majorana Corner Modes in a Second-Order Kitaev Spin Liquid
• Fractional topological phases in three-dimensional coupled-wire systems
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Flux crystals, Majorana metals, and flat bands in exactly solvable spin-orbital liquids
• Thermodynamic classification of three-dimensional Kitaev spin liquids
• Symmetry protected Z2-quantization and quaternionic Berry connection with Kramers degeneracy
• Kaleidoscope of topological phases with multiple Majorana species
• Changing topology by topological defects in three-dimensional topologically ordered phases
• Topological Insulators and Quantum Spin Liquids
• Topological Insulators and Superconductors from String Theory
• Time-reversal symmetric Kitaev model and topological superconductor in two dimensions
• Topological Insulators and Superconductors from D-branes
• Three-dimensional topological phases in a layered honeycomb spin-orbital model
• Determining quantum phase diagrams of topological Kitaev-inspired models on NISQ quantum hardware
• Fractional Chiral Hinge Insulator
• Higher-dimensional Jordan-Wigner Transformation and Auxiliary Majorana Fermions
• Exactly Solvable Topological Chiral Spin Liquid with Random Exchange
• Geometric Criterion for Solvability of Lattice Spin Systems
• Vison crystals, chiral and crystalline phases in the Yao-Lee model
• Realization of the Exactly Solvable Kitaev Honeycomb Lattice Model in a Spin Rotation Invariant System
• Localization of light in a three-dimensional disordered crystal of atoms
• Topological excitations in three dimensional Kitaev model
• Compass and Kitaev models -- Theory and Physical Motivations
• Exact Chiral Spin Liquids and Mean-Field Perturbations of Gamma Matrix Models on the Ruby Lattice
• A molecular diamond lattice antiferromagnet as a Dirac semimetal candidate
• Magnetic order and exchange couplings in the frustrated diamond lattice antiferromagnet MnSc${}_2$Se${}_4$
• Topological entanglement entropy of three-dimensional Kitaev model
• Bosonization of Majorana modes and edge states
• Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
• Pristine Mott Insulator from an Exactly Solvable Spin-1/2 Kitaev Model
• Induced topological order at the boundary of 3D topological superconductors
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Lacing topological orders in two dimensions: exactly solvable models for Kitaev's sixteen-fold way
• Three-dimensional spin-orbital liquids